HKCEE Mathematics

1.    Surds

Excel HSC Lectures: Surds????

2.    Quadratic Equations

Excel HSC Lectures: Equations    Linear and quadratic equations, algebraic and graphical methods (hyperbola).????
Review of Algebra Techniques - Factoring Quadratics    The method of completing the square and the quadratic formula
Solving Quadratic Equations (Live Mathematics on the Web)    Solving Quadratic Equations with JAVA.

Completing the square    Provide a tutorial applet for practicing completing the square (of form of x²+bx).

Completing the square    Provide a tutorial applet for practicing completing the square (general quadratic expression).

Quadratic, cubic and quartic equations     History about quadratic, cubic and quartic equations.

Quadratic Equation Solver   Solve quadratic equations and plot quadratic graphs inputted by user; also give information such as discriminant, parabola opening, vertex and factorization.

Equations (maths online)      The applet "Quadratic equations 2" may be used to show the effect of changing the values of p and q on the graph of y=x²+px+q.

The big function graph puzzle (maths online)     Users are required to recognize graphs out of more than 100 linear und quadratic functions by random and evaluates the success achieved.

3.    Graphs of Functions

Transformation of Functions (Tools for Analyzing Functions)    This tool demonstrates how the graph of a function f(x) changes under transformations such as f(x) + c, f(x+c), f(cx) where c is a constant.
Arithmetic Operations with Functions (Tools for Analyzing Functions)    This tool is used to graph functions which are arithmetic combinations of two functions. For example, given f(x) and g(x), it graphs f(x) + g(x).

Linear and Quadratic Graphs     Show the graphs of y=mx+c and y=nx² and the effects when the parameters change.

Mark's Mathematics Applets (The Sine Function)    The purpose of this applet is to help users to relate the coefficients in a sine function to the shape of its graph.

4.    Polynomials

Review of Algebra Techniques - Factoring Higher Order Polynomials    Synthetic division
Factoring a Polynomial (Tools for Algebraic Manipulation)    Factorize polynomials entered.

5.    Trigonometry

Mark's Mathematics Applets (The Sine Function)    The purpose of this applet is to help users to relate the coefficients in a sine function to the shape of its graph.

Frequently Asked Questions About Trigonometry     Provide many applets about basic trigonometry.

Trigonometry (Manipula Math with JAVA)     Many Java applets about trigonometry.

Functions 2 (Maths Online)     A good applet showing how the graphs of the three basic trigonometric functions are drawn (the applet "The graphs of sin, cos and tan").  Also provide two puzzle games in recognizing trigonometric graphs (the applets "Recognize functions 3" and "Recognize graphs 3,")

Trigonometry (maths online)     An applet on the sine formula.

6.    Sequences and Series

Excel HSC Lectures: Sequences and Series    Arithmetic and geometric progressions (including sum to infinity of G.P.), not many examples.????

7.    Approximate Roots of Equations

Finding Roots of Functions Using the Bisection Method and Newton's Method    Introduction to this two numerical methods and compare the methods.

Visual Calculus (Bisection Method)    Demonstrate the use of the bisection method to find roots of third degree polynomials. (Enter the coefficients, the interval and the numbers of steps, and the table of calculation will be generated.)
 

Last Updated: 18th October, 2000